Affiliation:
1. Department of Mathematics, Columbia University, New York, NY 10027, USA
Abstract
Vector bundles in positive characteristics have a tendency to be destabilized after pulling back by the Frobenius morphism. In this paper, we closely examine vector bundles over curves that are, in an appropriate sense, maximally destabilized by the Frobenius morphism. Then we prove that such bundles of rank 2 exist over any curve in characteristic 3, and are unique up to twisting by a line bundle. We also give an application of such bundles to the study of ample vector bundles, which is valid in all characteristics.
Publisher
World Scientific Pub Co Pte Lt
Cited by
5 articles.
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1. New constructions of nef classes on self-products of curves;Mathematische Zeitschrift;2022-08-16
2. Seshadri constants for vector bundles;Journal of Pure and Applied Algebra;2021-04
3. Meshing limit line of the conical surface enveloping conical worm pair;Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science;2019-09-29
4. ON MAXIMALLY FROBENIUS DESTABILISED VECTOR BUNDLES;Bulletin of the Australian Mathematical Society;2019-01-04
5. Frobenius stratification of moduli spaces of rank 3 vector bundles in positive characteristic 3, I;Transactions of the American Mathematical Society;2018-12-28